If all you are going to be shooting is .223 from an auto loader, I wouldn't screw with brass prep at all.
Go here:
Products
Buy yourself 500 or 1000 rounds of fully processed once fired military brass, and call it good.
You don't have to screw with case lube. You don't have to screw with crawling around on the ground scrounging cases, you don't have to screw with uniforming, trimming, primer crimp removing, etc.
Just run them though a neck sizer to uniform the mouths from any shipping dings, prime, charge and load.
And when you shoot them, leave them where they fall, because you have plenty.
As to polishing, I will say no, that is not necessary. Cleaning is absolutely necessary, as any grit on the case can get in the dies, and you don't want that. A tumbler is a good way to do that from a simplicity standpoint, throw the cases in, turn it on and walk away. There are other ways to clean brass, a web search will turn up a bunch of opinions.
Also, how much prep you do, largely depends on the application. If I am loading long range ammo, I will do prep the cases pretty extensively, clean the primer pockets, inside/outside chamfer and all that.
If I am loading some blasting ammo for a milsurp Mauser, I don't bother.
One of these days I need to do a blind test, load up 20 rounds with all the anal case prep, and 20 rounds without and have my wife box them up without telling me which is which. See if I can tell the difference.